Introduction to Crystal Growth: Principles and Practice

346 Pages·2014·8.587 MB·English

by  H L Bhat

Introduction to
CRYSTAL GROWTH
Principles and Practice

Introduction to
CRYSTAL GROWTH
Principles and Practice
H. L. Bhat
Former Professor of Physics
Indian Institute of Science
Bangalore
and
Visiting Professor
Centre for Nano and Soft Matter Sciences
Bangalore
CRC Press
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To my parents

Contents
Preface .....................................................................................................................xv
Author ..................................................................................................................xvii
Section I Principles
1. Introduction .....................................................................................................3
What Are Crystals? ..........................................................................................3
Why Single Crystals? .......................................................................................4
Why Should One Grow Crystals? .................................................................6
Historical Perspective ......................................................................................6
Organization of the Book ..............................................................................10
References .......................................................................................................11
2. Nucleation Phenomena ................................................................................13
Critical Supersaturation ................................................................................13
Homogeneous (Spontaneous) Nucleation ..................................................15
Heterogeneous Nucleation ...........................................................................19
Nucleation on a Substrate .............................................................................20
Nucleation of a Crystalline Material ...........................................................21
Equilibrium Shape of Anisotropic Nuclei ..................................................22
References .......................................................................................................23
3. Crystal Growth Mechanisms .....................................................................25
Early Theories .................................................................................................25
Two-Dimensional Layer Growth Mechanism ...........................................28
Surface Nucleation .........................................................................................32
Verification ......................................................................................................35
References .......................................................................................................36
4. Defects in Crystals .......................................................................................37
Point Defects ...................................................................................................37
Vacancy .......................................................................................................38
Schottky Defect .........................................................................................39
Frenkel Defect ............................................................................................39

Interstitial Defect .......................................................................................40
Substitutional Defect ................................................................................40
Color Centers .............................................................................................40
Line Defects or Dislocations .........................................................................41
Theoretical Estimation of Critical Shear Stress ....................................43
vii
viii Contents
Refinement in Calculation of Critical Shear Stress ..............................45
Edge Dislocation ........................................................................................46
Screw Dislocation ......................................................................................48
Mixed Dislocation .....................................................................................49
Burgers Vector ...........................................................................................49
Motion of Dislocations .............................................................................50
Energy of a Straight Screw Dislocation .................................................51
The Force on a Dislocation When a Shear Stress Is Applied ..............54
Dislocation Multiplication .......................................................................56
Low-Angle Grain Boundaries .................................................................57
Planar Defects.................................................................................................58
Stacking Faults ...........................................................................................58
Twin Boundaries .......................................................................................60
Grain Boundaries in Polycrystals ...........................................................61
Bulk Defects ....................................................................................................61
References .......................................................................................................62
5. Dislocations and Crystal Growth .............................................................65
Screw Dislocation Theory of Crystal Growth ...........................................65
The Theory .................................................................................................66
Experimental Verification ........................................................................68
Growth from Solution ..............................................................................69
Shape of Growth Spirals ..........................................................................71
Interaction of Growth Spirals ..................................................................72
Vapor–Liquid–Solid Mechanism of Crystal Growth ................................72
Dendritic Growth ...........................................................................................75
References .......................................................................................................76
6. Phase Diagrams and Crystal Growth ......................................................79
Latent Heat ......................................................................................................79
Gibbs’s Free Energy .......................................................................................80
Chemical Potential .........................................................................................81
Gibbs’s Phase Rule .........................................................................................82
Phase Diagrams .............................................................................................83
Single-Component Systems .....................................................................83
Water ......................................................................................................84
Diamond ................................................................................................85
Two-Component Systems ........................................................................86
Two-Component Solid Solutions .......................................................86
Lever Rule ..............................................................................................87

Crystallization Path .............................................................................88
Two-Component Eutectic Systems ....................................................89
Two-Component Peritectic Systems ..................................................91
Three-Component Systems .....................................................................91
Concentration–Temperature Phase Diagrams (Solubility Curves) ....94
Contents ix
Typical Phase Diagrams................................................................................96
Sodium p-Nitrophenolate ........................................................................96
Gallium Antimonide ................................................................................98
Lithium Niobate ......................................................................................101
Cesium Lithium Borate ..........................................................................101
Potassium Titanyl Phosphate (K O–P O –TiO System) ....................104
2 2 5 2
References .....................................................................................................105
Section II Practice
7. Growth from the Solid Phase ..................................................................111
Introduction ..................................................................................................111
Solid–Solid Growth Methods .....................................................................112
Grain Growth ...........................................................................................112
Strain-Annealing Technique .................................................................116
Solid-State Phase Transformation .........................................................120
General Conclusions ....................................................................................121
References .....................................................................................................122
8. Growth from the Melts ..............................................................................123
Introduction ..................................................................................................123
Bridgman–Stockbarger and Related Techniques ....................................124
General Considerations ..........................................................................124
Vertical Bridgman Method ....................................................................124
Vertical Gradient Freeze Technique .....................................................125
Horizontal Bridgman Method ..............................................................126
Equipment ................................................................................................127
Furnaces ...............................................................................................127
Electrodynamic Gradient Freeze Furnace ......................................128
Crucibles ..............................................................................................129
Mechanical Movement ......................................................................130
Melt–Solid Interface Shape ....................................................................131
Examples ..................................................................................................133
Growth of Indium Antimonide ........................................................134
Materials Synthesis ............................................................................135
Crystal Growth ...................................................................................135
Limitations ...............................................................................................139
Czochralski and Related Techniques .......................................................140
Equipment ................................................................................................142

Crucibles ..............................................................................................143
Heaters .................................................................................................144
Diameter Control ....................................................................................144
Example ....................................................................................................145
Growth of Congruent Lithium Niobate Crystals ..........................146
x Contents
Refined Processes ....................................................................................148
Growth of Stoichiometric Lithium Niobate ....................................149
Liquid Encapsulation Technique .....................................................149
Shaped Crystal Growth ..........................................................................151
Stepanov Method ...............................................................................152
Edge-Defined, Film-Fed Growth ......................................................153
Micro-Pulling-Down Method...........................................................153
Zone-Melting Techniques ...........................................................................155
Normal and Equilibrium Freezing .......................................................155
Principle of Zone Refining .....................................................................159
Segregation due to Single-Zone Pass ...............................................159
Segregation due to Multiple-Zone Passes .......................................160
Zone Leveling .....................................................................................161
Zone Freezing .....................................................................................161
Zone Refining as a Technique for Crystal Growth ............................162
Horizontal Configuration .................................................................162
Material Transport .............................................................................163
Vertical Configuration: Floating Zone Technique .........................164
Zone Stability ......................................................................................165
Example ....................................................................................................166
Material Synthesis and Preparation of Ingots ................................166
Typical Growth Run ...........................................................................167
Flame Fusion Technique .............................................................................170
Technical Considerations .......................................................................172
Seed Preparation ................................................................................172
Burner Design .....................................................................................172
Powder Preparation and Feeding ....................................................173
Growth Chamber ...............................................................................174
Typical Crystals Grown..........................................................................174
Crystal Growth by the Arc Fusion Technique .........................................175
Growth by the Skull-Melting Technique ..................................................176
References .....................................................................................................178
9. Growth from Liquid Solutions ................................................................183
Introduction ..................................................................................................183
Growth from Aqueous Solution ................................................................183
Solution and Solubility ...........................................................................184
Choice of Solvent .....................................................................................185
Additives ..................................................................................................187
Nucleation ................................................................................................187

Achievement of Supersaturation ..........................................................188
Apparatus .................................................................................................188
Mason-Jar Method ..............................................................................188
Holden’s Rotary Crystallizer ............................................................190
Temperature Differential Method ...................................................193